Multilevel Monte Carlo in approximate Bayesian computation

Multilevel Monte Carlo in approximate Bayesian computation

Jasra, Ajay, Seongil Jo, David Nott, Christine Shoemaker, and Raul Tempone. "Multilevel Monte Carlo in approximate Bayesian computation." Stochastic Analysis and Applications, Volume 37, no.3 (2019): 346-360.​
Ajay Jasra, Seongil Jo, David Nott, Christine Shoemaker, Raul Tempone.
Approximate Bayesian computation, multilevel Monte Carlo, sequential Monte Carlo.
2019
​In the following article, we consider approximate Bayesian computation (ABC) inference. We introduce a method for numerically approximating ABC posteriors using the multilevel Monte Carlo (MLMC). A sequential Monte Carlo version of the approach is developed and it is shown under some assumptions that for a given level of mean square error, this method for ABC has a lower cost than iid sampling from the most accurate ABC approximation. Several numerical examples are given.